Ferromagnetism in two-dimensional ${\mathrm{Fe}}_3\mathrm{Ge}{\mathrm{Te}}_2$; Tunability by hydrostatic pressure

We studied the effect of hydrostatic pressure on the magnetic properties of the highly anisotropic van der Waals ferromagnetic metal ${\mathrm{Fe}}_3\mathrm{Ge}{\mathrm{Te}}_2$ (FGT) with the field applied along the easy axis. The paramagnetic-to-ferromagnetic transition occurs at the Curie temperature $T_c=180\mathrm{K}$ at ambient pressure, and $T_c$ decreases monotonically by up to 15 K as the pressure increases up to 1.44 GPa, while the magnetization is suppressed by the pressure. By using high-pressure x-ray diffraction techniques, we found that the Fe-Fe bond lengths tend to decrease, and the Fe-Ge(Te)-Fe bond angles deviate away from ${90}^{\circ }$ under hydrostatic pressures, indicating the modification of the exchange interactions. First-principles calculations further confirm the pressure effects. These results suggest that the competition between direct-, super-, and double-exchange interactions plays a crucial role in the pronounced magnetic response under the hydrostatic pressure, i.e., the direct-exchange becomes stronger at a higher pressure and, hence, leading to increased antiferromagnetic components and thus deceased $T_c$. The highly tunable magnetic properties under hydrostatic pressure in this system provide robust routes for spin manipulation in low-dimensional material systems.

Figure 1

(a) Atomic structure of ${\mathrm{Fe}}_3\mathrm{Ge}{\mathrm{Te}}_2$ (FGT). Fe1 and Fe3 represent the Fe ions at two different layers along the $c$ axis. Fe1 (Fe3) and Fe2 are the two types of Fe ions at two inequivalent sites in the oxidation state +3 and +2, respectively. The different sizes and colors of the atom models for Fe1, Fe2, and Fe3 are guides to the eye. (b) Hysteresis loops for FGT at ambient pressure with the field applied along the $c$ axis ($H\parallel c$) and perpendicular to the $c$ axis ($H\perp c$) at a representative temperature of 100 K after linear background subtraction.

Figure 2

(a) Temperature dependence of the zero-field-cooling magnetization for ${\mathrm{Fe}}_3\mathrm{Ge}{\mathrm{Te}}_2$ (FGT) at different hydrostatic pressures with the external field (100 Oe) applied along the $c$ axis. The inset shows $dM/dT$ as a function of temperature for different pressures. (b) The pressure dependence of $T_c$, where $T_c$ is estimated from the minimum point of $dM/dT$. The dashed line is the guide for the eye. (c) The hysteresis loops were obtained at 100 K with applying pressure. The inset is an enlarged area for the details of the changes in the $M_s$. (d) The variation of $M_s$ for FGT with increasing the pressure. The magnetic properties are restored when the pressure is released back to the ambient pressure.

Figure 3

(a) In situ x-ray diffraction (XRD) patterns of ${\mathrm{Fe}}_3\mathrm{Ge}{\mathrm{Te}}_2$ (FGT) under high pressure from 0 to 1.7 GPa at room temperature. The black solid lines are the calculated results using Rietveld refinement method (for details, see Supplemental Material Fig. S2 [39]). (b) and (c) are pressure-induced peak shifts of (002) and (101), respectively.

Figure 4

(a) The lattice constant $a$ and $c$ calculated from the refined x-ray diffraction (XRD) pattern as a function of the applied pressure. The dashed lines are the guide for the eye. (b) Pressure dependence of the bond angle ${\theta }_1$ (Fe2-Ge-Fe3), ${\theta }_2$ (Fe1-Ge-Fe1), and ${\theta }_3$ (Fe1-Te-Fe1). The inset shows the three different paths for double-exchange interaction between ${\theta }_1$ (Fe2-Ge-Fe3), and super-exchange interaction between the nearest neighbor atoms ${\theta }_2$ (Fe1-Ge-Fe1) and ${\theta }_3$ (Fe1-Te-Fe1).

Figure 5

(a) Three magnetic configurations including the ferromagnetic (FM) structure and two antiferromagnetic (AFM) structures. (b) The calculated evolution of the $T_c$ for ${\mathrm{Fe}}_3\mathrm{Ge}{\mathrm{Te}}_2$ (FGT) under pressure. The energy difference between FM and AFM2, $\mathrm{\Delta }E=E\left(\mathrm{FM}\right)-E\left(\mathrm{AFM}2\right)$ is calculated from the changes of the lattice parameters. The decrease in $\left|\mathrm{\Delta }E\right|$ indicates the weakened FM coupling with applying pressure, thus the $T_c$.

Figure 6

Pressure-induced changes of the magnetization for per Fe1(Fe3), Fe2, and average Fe atom.